Parametric study on nonlinear vibration of FG-GNPRC dielectric beam with Kelvin–Voigt damping

Abstract

Internal damping plays an essential role in the structural behaviors of composites. This paper adopts Kelvin–Voigt model to investigate the effects of the internal damping on nonlinear vibration of functionally graded graphene nanoplatelet reinforced composite (FG-GNPRC) beam with dielectric properties. Within the framework of Timoshenko beam theory, governing equations for the vibration of the damped beam are developed by incorporating the internal damping in terms of energy. The governing equations are discretized by differential quadrature (DQ) method after state–space​ transformation and then solved numerically by direct iteration. The validated results demonstrate that the nonlinear natural frequency of the structure is highly dependent on the shear proportionality constant of the Kelvin–Voigt internal damping. It is found when the beam is subjected to higher voltage, the functionally graded distribution of the reinforcing filler enables the composite structure to be more stable compared to uniform distribution. Moreover, the nonlinearity of the structure is more sensitive to DC voltage for composite beams with smaller slenderness ratio and thickness.